Question

The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School A rented and filled 3 vans and 6 buses with 291 students. HighSchool B rented and filled 9 vans and 12 buses with 633 students. Each van and each bus carriedthe same number of students. Write a SOE and solve it to find the number of students ineachvan and in each bus.

Answer 1

In High school A 3 filled vans: 51 students and 102 students in buses, In High School B, 153 students in vans and 480 in buses.

1) Given the data:

High School A

3 vans + 6 buses, 291 students

High School B

9 vans, 12 buses and 633 students

2) We can write the following system of equation:

3v +6b = 291

9v +12b=633

Let's use the Elimination/Addition Method to solve that equation

3v +6b = 291 x (-2)

9v +12b=633

Add both equations simultaneoulsy:

-6v -12b = -582

9v +12b=633

----------------------------

3v =51

v=17

Plugging that value into the simplest equation

3(17) +6b = 291

51 +6b=291 Subtract 51 from both sides

6b=240

b=40

2) So there were 40 buses and 17 vans. In High school A 3 filled vans: 51 students and 102 students, In High School B, 153 students in vans and 480 in buses.